# Measuring speed

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1. Jul 25, 2015

### Stephanus

Dear PF Forum,
I'd like to know how to measure speed only by doppler effect.
What if we don't know the frequency?
What if we don't know the distance?

If we look this diagram on our computer screen, we'll know everything. Distance, speed, time dilation event relative simultaneity of event. But here, there are no relative simultaneity of events, because they are all time like.
Here, Green (G) will send a signal to Blue (B) everytime G receives B signal.
And B can't rely on the frequency of G signal, it might, it might not be same. For example B signal is at 100 MHz, and G send its own signal regardless what B sends, say 50MHz.
And this is all that B can see:
B sends its clock time then, G sends back B's clock time.
Code (Text):
Events Time A Diff   Freq  Read B
E1        700  ..       1   -1100
E2        900  200  1 > 4    -900
E3        950   50      4    -700
E4       1125   …               0
E5       1175   50      4     200

B can work out the speed by this formula
$f = \frac{1+V}{1-V}; 4 = \frac{1+V}{1-V}; V=\frac{3}{5}$
Time A column is B's clock when Blue receives the signal.
Read B column is the clock when Blue sent the signal.
Ok, it makes sense. Once the light cone from G entering B world line, the frequency changes to 4, forever.
Here at E2, actually Blue doesn't have to wait until E3, to know that the frequency changes. Blue could have sends signal at 1 pico seconds interval instead of 200 seconds interval. So right after E2, Blue can already detect the changing frequencey.

But I see something strange with this diagram.

Here is what B reads from the signal from G

Code (Text):
Events Time A    Diff      Freq   Read B
E1       -200      …          1    -2000
E2          0     200    1 -> 2    -1800
E3        100     100         2    -1600
E4        900      …                   0
E5        950      50         4      200

The instant Blue moves the frequency changes to 2.
After sometime the signal from the time when B moves is received by B, the frequency changes to 4.
So, there are times between (E2 and E4) when Blue miscalculates the speed if using the same method as above picture.
E4 is the event when B receives the bounce back signal from when B started to move.
When F = 2, V is 1/3
When F = 4, V is 3/5
Where did I go wrong?

Thanks.

Last edited: Jul 25, 2015
2. Jul 25, 2015

### Mentz114

The speed can be calculated by using a spectrometer to measure the change in the frequency of the light/radar pulse that is sent.

The distance to the reflection event can be found by timing the light/radar pulse.

So if blue has a radar gun that measures the Doppler the distance and speed can be got from a single pulse.

#### Attached Files:

• ###### dop-dist11.png
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3. Jul 25, 2015

### Stephanus

But, could you please take a look at diagram 2? Because the change of frequency is not consistent.

4. Jul 25, 2015

### Mentz114

Blue starts moving at t=0 so naturally the freqency changes.

5. Jul 25, 2015

### Stephanus

And naturally Blue mistakenly calculate the speed until t=900, where the signal from Blue when starts move is received.

6. Jul 25, 2015

### Mentz114

If the receiver or sender accelerates during the measurement then the process won't work.

Why are you making difficulties ? What don't you understand ?

7. Jul 25, 2015

### Stephanus

I understand now.

8. Jul 25, 2015

### Stephanus

No wait,
I think we should correct it

9. Jul 25, 2015

### Mentz114

No. Doppler is reciprocal. If the relative velocity is not constant the formula does not apply as it stands.

10. Jul 25, 2015

### Stephanus

It really clears the path for me. Thanks.